LONDON — Addise Mekonen was working a night shift on Friday when he learned from television news that his apartment was one of 650 London flats being evacuated in the middle of the night amid fears that it might be as dangerous as Grenfell Tower, which had been incinerated in the deadliest blaze in Britain in more than a century.

After sitting for hours on a bench in a corner of an emergency relief center near the five towers that had been evacuated in Camden, north London, Mr. Mekonen had another night shift looming on Saturday, but no bed to sleep in.

“I’m really shocked,” he said as he and dozens of other residents waited to discover where they would spend the coming days and whether their homes were now considered death traps because they were in tower blocks that had failed fire safety tests.

“In the world’s fifth-largest economy, this is appalling,” added Mr. Mekonen, a resident of the Bray tower block who is originally from Ethiopia. “This wouldn’t happen in Africa.”

More than a week after the blaze gutted the 24-story Grenfell Tower, killing at least 79 people, the aftershocks are rippling across Britain as the nation grapples with the unsettling prospect that thousands of families may be at risk of a similar fate, and could have been for years.

Camden Council’s extraordinary evacuation of thousands of people, who had to grab clothes and whatever else they could find and leave quickly in the dead of night, is a jarring example of a gathering political and social crisis.

The fact that many of the affected residents live in housing projects and are among the poorest in a rich Western nation has added to the discomfort of Prime Minister Theresa May, who promised to tackle social injustice last year when she took power.

For some, the blackened remains of Grenfell Tower, close to some of the city’s most expensive homes, has also become a symbol of the economic and class divides in Britain’s globalized capital city. And there is angry suspicion that lives could have been saved had relatively small sums of additional money been spent on Grenfell for nonflammable material.

Britons were already on edge after two fatal terrorist attacks in London and one in Manchester in less than three months, but the London fire disaster, along with the sense that such a horrific accident might have been avoided, has deepened the mood of gloom and soul-searching.

Britain faces what the leader of the Birmingham City Council, John Clancy, told the BBC on Saturday was a “national emergency.”

“The dreadful events in London have understandably triggered an outburst of public anger and demands that councils need to do far more to protect tenants living in high-rise blocks,” Mr. Clancy said.

So far, samples from 27 tower blocks in 15 areas in England have shown that the cladding, or aluminum facade, wrapped around the buildings is unsafe, the government said. Other buildings, including privately owned blocks, hospitals, schools and hotels, may also be affected. One hotel chain, Premier Inn, told the BBC that it was “extremely concerned” about cladding at buildings in Maidenhead, Brentford and Tottenham.

Councils are scrambling to address the problem. Mr. Clancy’s city, for example, plans to equip its 213 high-rise residential buildings with sprinklers. Several others have begun removing the type of cladding that is thought to have helped turn Grenfell into a fireball.

The Camden Council, determined that there should be no repeat of the Grenfell catastrophe, insisted on Saturday that it had acted swiftly once it became clear that the homes were fire risks.

“Grenfell changes everything, and I just don’t believe we can take any risk with our residents’ safety,” said Georgia Gould, the council leader. She added that the fire service had “told us they could not guarantee our residents’ safety in those blocks.”

So late Friday night, waking some residents, the council ordered families to leave their homes. They were encouraged to stay with friends and family or were offered hotel rooms, and some slept in emergency reception centers.

Despite the warnings, more than 80 people have refused to move. Among some residents here, the sudden evacuation suggested blind panic on the part of city officials.

“I am very, very uncomfortable and worried,” Aida Asik Austin said outside the Burnham block, where she, her husband and her son, 11, had spent the night, despite being urged to leave by the police, who had banged on her door at midnight.

Ms. Austin now says she has no option but to vacate the apartment, since the gas supply will be disconnected. But she worries that she may be sheltered miles away from her son’s school and her husband’s workplace.

Mary Kelly, a resident of the Bray block, told of how she had been watching television when her son called to tell her that her building was being evacuated. “They are not telling me anything,” said Ms. Kelly, who spent the night at the relief center, declining a hotel room in order to be closer to her home.

Such scenes of displacement and discomfort pose a growing political risk for Mrs. May, who was already weakened after losing her parliamentary majority in an election this month.

The prime minister was widely accused of fumbling the original response to the Grenfell Tower disaster, initially failing to meet with shocked and angry survivors. Despite subsequently devoting much time and attention to dealing with the aftermath, her government has rarely seemed in control of events.

On Thursday, there was confusion about the number of tower blocks thought to have hazardous cladding similar to Grenfell Tower’s. Downing Street at first suggested that 600 tower blocks, and thousands of families, were at risk — though that proved to be the total number of high-rise homes with any form of cladding.

The government is still unable to say whether the cladding at Grenfell had complied with British building regulations. To add to the worries, landlords of privately owned homes have been only encouraged, not compelled, to send in samples of cladding for testing.

Downing Street has said that it is investigating whether defective cladding has been used on schools and hospitals, while adding that these tend to be shorter buildings and therefore less dangerous.

On Saturday, Sajid Javid, the secretary of state for communities and local government, told Sky News that the evacuation in Camden had been prompted by concerns beyond cladding, including problems with insulation, fire doors and gas piping.

Outside the Burnham block in Camden on Saturday, Claire-Louise Leyland, a Conservative Party councilor, echoed that message, and defended the council’s emergency action. Ms. Leyland had spent much of Friday night trying to persuade residents to evacuate their homes, mostly — but not always — with success.

“If you are woken up, you are shocked, and people struggle to come to terms with what has happened,” she said of the residents’ reaction.

Grenfell Tower, she said, had been such a traumatic event because it undermined some basic assumptions about how to keep people safe. “The fire was so unprecedented,” she said. “We have had to question all our procedures.”